An object wouldn't render in cycles (all solutions on the topic I found don't work)
The cutting plane is somehow overlapping geometry and causing Z Fighting artifacts.

Your $Intitial$ object as a Boolean modifier invisible to viewport and visible to rendering leading to different results.

Your scene also as a multitude of unrelated issues like using Hemi lamps which aren't truly supported in Cycles and a Sun lamp which doesn't really seem to be doing much besides illuminating the background, since you are using an ambient occlusion shader on your objects which doesn't interact with scene lighting.